These measures are symplectic and orthogonal analogues of the Poissonized Plancherel measureThe choice of \(2\theta \)  inside \(sp/o\)  is to facilitate the computations, but could be replaced by any other parameter different from \(0, \theta \)  if one is willing to do a change of variables at the end. The empty specialization 0 for \(sp/o\)  is also interesting, and related to Section 7 of [1]}, but we defer this to another time and space.. For fixed \(\theta \)  they are not necessarily positive. However as \(|\lambda |\)  increases \(P_{sp/o}(\lambda )\)  does become positive since \(sp/o_{\lambda }(pl_{2 \theta })\)  is a polynomial in \(\theta \)  with leading monomial \(\theta ^{|\lambda |}\)  having positive coefficient due to the Jacobi–Trudi formulas (REF ) for \(sp\)  and \(o\) .
